tool for imaging a downhole environment

ABSTRACT

The invention is concerned with a tool and method for imaging a formation through a substantially non-conductive medium. The tool comprises first circuitry for injecting a current into the formation, wherein a complex impedance to the current is measured. Second circuitry for determining a phase angle of an impedance of the non-conductive medium and third circuitry for determining a component of the complex impedance that is orthogonal to the phase angle.

FIELD OF THE INVENTION

The invention relates to a tool for imaging a formation, and inparticular but not exclusively, a tool for imaging a formation through asubstantially non-conductive medium.

BACKGROUND OF THE INVENTION

For oilfield and hydrocarbon exploration it is particularly useful tohave a tool that is capable of scanning a subsurface geologicalformation and to convey data representing the various strata andhydrocarbons that constitute a subsurface geological formation.Specifically, after drilling a borehole down into the earths crust, itwould be useful to have downhole tools that are capable of being runalong the borehole wall and scanning the surrounding formation toprovide an image of the formation's properties to a user on the surface.Equally, it is useful to have such a tool mounting on or close to adrill tip so that the formation can be imaged as the drill penetratesinto the earths crust. This would enable a user to measure and/or imagevarious formation parameters close to or ahead of the drill bit and fromthere get the latest information about the downhole formation, whichmight impact on the direction being drilled.

Tools using current injection are known, for example U.S. Pat. No.4,468,623, U.S. Pat. No. 4,614,250, U.S. Pat. No. 4,567,759, U.S. Pat.No. 6,600,321, U.S. Pat. No. 6,714,014 or U.S. Pat. No. 6,809,521; thatuse current injection measurements in order to obtain micro-electricimages of a borehole wall, the borehole penetrating geologicalformations.

Such tools inject AC current into the formation from one or more smallelectrodes (called “buttons”) and measure the current from each buttonand the voltage between the imaging buttons and the return electrode. Inconductive mud (for example, water-based) the imaging button issurrounded by a guard electrode to force the current into the formation.In non-conductive (oil-based) mud such a guard is not necessary if theformation is more conductive than the mud at the frequency of operation.The imaging buttons plus guard electrode (if present) compose theinjector. The impedance (voltage/current) seen by each button isindicative of the resistivity of a small volume of formation in front ofeach button. The area of the return electrode is usually much largerthan the size of the injector, in order that the current tube spreadsout between the injector and return to ensure first a high sensitivityand good resolution in front of the imaging buttons and second lowsensitivity and resolution in front of the return electrode.

Such tools can be adapted for wireline use, in which an array of imagingbuttons is at equipotential with a guard electrode on a pad (laterologprinciple) and the return is on a distant part of the tool mandrel. Suchtools operate at frequencies in the range 1-100 kHz where the formationgenerally has a resistive character and dielectric effects can beneglected except at very high resistivities.

Such tools can be adapted as logging-while drilling tools, which areable to achieve full coverage of the borehole with a limited number ofelectrodes by drill-string rotation. Laterolog principles are used,sometimes with additional focusing by hardware or software.

However, the use of such tools in non-conductive oil-based mud is oflimited use because the impedance measured is generally dominated by themud impedance between the injection electrode and formation that is inseries with the formation impedance. Reasonable images can be obtainedin high-resistivity formations, i.e. above about 1000 Ω·m, but poorimages result in formations having a lower resistivity.

Broadly speaking, two approaches have been adopted to enable betterimaging through oil-based mud in formations of low resistivity.

The first approach relies on a different measurement principle, thefour-terminal method as described in U.S. Pat. No. 6,191,588. Here thecurrent is generated in the formation using two large electrodes nearthe ends of a pad and potential differences in the formation aremeasured using pairs of small electrodes at the centre of the pad. Usingthis technique the resolution is worse than conventional currentinjection tools because it is determined by the separation of the pairof voltage electrodes (rather than the size of the current injectionelectrode). Also, this technique is insensitive to events (bedding,fractures etc) parallel to the current flow (usually parallel to theborehole axis).

The second approach is to increase the frequency of injection-type toolsin order to reduce the mud impedance, i.e. U.S. Pat. No. 2,749,503.

At high frequencies, various processing techniques have been suggestedto reduce the influence of the non-conductive mud between the pad andthe borehole. U.S. Pat. No. 7,066,282 proposes measuring the real partof the impedance seen by the button, while U.S. Pat. No. 6,809,521, U.S.Pat. No. 7,394,258 and U.S. Pat. No. 7,397,250 all require making atleast one mathematical approximation based on the mud impedance beingessentially imaginary, or the formation impedance being essentiallyreal, or using more than one frequency and assuming various mudproperties are independent of frequency. These approximations havelimited ranges of validity, since they do not adequately account for theelectrical properties of the rocks and muds.

It is therefore desirable to provide a tool that is able to reduce theinfluence of the non-conductive mud medium when using a currentinjection principle and to avoid the previously-mentioned limitations.

SUMMARY OF THE INVENTION

According to a first aspect of the present invention there is provided atool for imaging a formation through a substantially non-conductivemedium, the tool comprises: first circuitry for injecting a current intothe formation, wherein a complex impedance to the current is measured;second circuitry for determining a phase angle of an impedance of thenon-conductive medium; and third circuitry for determining a componentof the complex impedance that is orthogonal to the phase angle.

According to a further aspect of the present invention there is provideda method for measuring a component of an impedance of a formationthrough a substantially non-conductive medium, the method comprising:injecting a current in the formation; measuring a complex impedance tothe current; determining a phase angle of an impedance of thenon-conductive medium; and determining the component of the compleximpedance that is orthogonal to the phase angle.

According to yet a further aspect of the invention there is provided anapparatus for imaging a formation through a substantially non-conductivemedium interposed between the apparatus and the formation; the apparatuscomprising: an imaging button spaced at a first distance from theformation for injecting a first current into the formation; a mud buttonspaced at a second distance from the formation for injecting a secondcurrent into the formation; and a processing unit for determining afirst impedance from said first current and a second impedance from saidsecond current, taking a difference between the first and the secondimpedance, determining the phase angle from the difference, anddetermining the component of impedance from the imaging button that isorthogonal to the phase angle.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example and not limitedto the accompanying figures, in which like references indicate similarelements:

FIG. 1 shows a partial cross-section view of a part of a typicalhigh-frequency current injection tool;

FIGS. 2 a and 2 b respectively show examples of imaging tools designedfor water-based mud and oil-based mud respectively;

FIG. 3 shows an equivalent circuit of impedances as seen by an imagingelectrode;

FIG. 4 shows a further reduced equivalent circuit of impedances as seenby an imaging electrode;

FIGS. 5 a, 5 b and 5 c show typical impedance vector diagrams inoil-based mud in different conditions of frequency and formationresistivity;

FIG. 6 a shows the reduced circuit of the impedances;

FIG. 6 b shows the vector diagram of the impedances;

FIG. 6 c shows a determination of the orthogonal and parallel componentsaccording to one embodiment;

FIGS. 7 a and 7 b show equivalent circuits for measurement of mudimpedance using recessed buttons according to an embodiment;

FIG. 8 shows the mud impedance measurement in vector form;

FIG. 9 shows a high frequency imaging pad with recessed mud buttonsaccording to an embodiment;

FIG. 10 shows results of amplitudes and phase measurements at threestandoffs;

FIG. 11 shows results of orthogonal and parallel components of impedancemeasured at three standoffs;

FIG. 12 shows an imaging pad with only a single recessed buttonaccording to a further embodiment;

FIG. 13 shows an example of a wireline application;

FIG. 14 shows an alternative embodiment for determining the mudimpedance;

FIG. 15 shows another embodiment of button placement on a pad;

FIG. 16 shows yet another embodiment of button placement on a pad;

FIG. 17 shows a cut-off section for implementing the recessed buttonplace of the embodiment in FIG. 16; and

FIG. 18 shows another embodiment with a plurality of electrodes forobtaining a profile of the borehole wall.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows a partial cross-section of the current injection principle.Specifically, there is shown a tool located in mud 2 down a boreholesurrounded by a rock formation 4. There is a button, or injectionelectrode, 10 which is responsible for injecting current into theformation 4 and returns to the tool via a return electrode 6. Theimaging button 10 has a sensitive imaging region 8 and is insulated 12from a guard electrode 14.

Specifically, there is a shown a voltage source 18 that generates apotential difference between the imaging button 10 and the returnelectrode 6. Since these electrodes are a different potential, a currentis injected into the formation which follows along the paths indicated.FIG. 1 also shows an ammeter 20 for measuring the current injected intothe formation. In practice, this might take the form of a small knownresister, where the current can be determined from the known voltageacross the resistor divided by the known resistance itself.

Moreover, it is possible to determine the complex impedance Z bydividing the known generated complex voltage by the known complexcurrent. By complex is meant that the relevant parameter, i.e. voltageV, current I or impedance Z, have an in-phase (or real) component aswell as a quadrature (imaginary) component if represented on Cartesianaxes. Alternatively, if a polar co-ordinate system is used, complexmeans the relevant parameters can also be represented in terms of anamplitude and phase component.

FIGS. 2 a and 2 b show a high frequency imaging tool that are designedfor water-based mud and oil-based mud respectively.

FIG. 3 shows an approximate electrical equivalent circuit of theimpedances seen by an imaging button in non-conductive oil-based mud.Specifically, the impedance measured is of the mud impedance Zm, theformation impedance Zf and the mud return impedance Zmr, in series.

Current injection tools are usually designed so the area of the returnelectrode is much greater than the area of the injection electrode sothat the measurement is not sensitive to the formation adjacent to thereturn. This being so, the mud impedance between the return andformation Zmr can usually be neglected compared to the mud impedancebetween the injection electrode and the formation Zm. In other words:Zm>>Zmr.

FIG. 4 shows the revised impedance model neglecting the mud returnimpedance Zmr as well as splitting the impedances into their respectivecapacitive and resistive components. Specifically, the formationimpedance Zf is represented by the formation capacitance Cf in parallelwith the formation resistance Rf. The mud impedance Zm is represented bythe mud capacitance Cm in parallel with the mud resistance Rm.

The total impedance Z is given by

Z=Z _(m) +Z _(f)

where

Z _(m)=(d _(m) /A _(m))/σ*_(m)

Z _(f)=(d _(f) /A _(f))/σ*_(f)

The complex conductivity (also called admittivity) σ* is given by:

σ*=σ+iω∈

and d is the effective distance along the current path, A is theeffective area of the current path and ∈ is the permittivity.

Z_(m) and Z_(f) can be thought of as parallel R-C circuits as shown inFIG. 4 with:

R _(m) =d _(m)/(A _(m)·σ_(m))

C _(m)=∈_(m) A _(m) /d _(m)

R _(f) =d _(f)/(A _(f)·σ_(f))

C _(f)=∈_(f) A _(f) /d _(f)

Concerning the mud, d_(m) is the thickness of the mud medium between theimaging electrode and the formation while A_(m) is the area of theelectrode. If the mud medium is 2 mm thick and the electrode has aradius of 2.5 mm, A_(m)/d_(m)˜10⁻² m. Concerning the formation, thefactor A_(f)/d_(f) is typically 10 to 100 times smaller than A_(m)/d_(m)because the penetration depth in the formation d_(f) is much greaterthan the thickness of the mud medium d_(m)

The phase angles of the impedances are given by:

φ_(m)=−tan⁻¹(ω∈_(m)/σ_(m))

and

φ_(f)=−tan⁻¹(ω∈_(f)/σ_(f))

for the mud and formation respectively. Typical values of ω/∈σ for rockand mud are taken from laboratory measurements.

FIG. 5 shows typical impedance vectors when the formation resistivity issufficiently low that the mud impedance is greater than the formationimpedance. The only assumption that can be made is that the phases ofthe mud and formation impedances are different.

Specifically, FIG. 5( a) shows a conventional FMI operating at around 10kHz in oil-based mud with a formation resistivity of about 100 Ω·m. Themud impedance is much greater than the formation impedance, the mudimpedance phase is in the range −90 to −30 deg and the formation phaseis very close to zero (pure resistance).

FIG. 5( b) shows a high-frequency FMI operating at around 50 MHz inoil-based mud with a formation resistivity of about 1 Ω·m. The mudimpedance is much greater than the formation impedance, the mudimpedance phase is in the range −80 to −90 deg and the formation phaseis close to zero (pure resistance).

FIG. 5( c) shows a high-frequency FMI operating around 50 MHz inoil-based mud with a formation resistivity of about 10 Ω·m. The mudimpedance is greater than the formation impedance, the mud impedancephase is in the range −80 to −90 deg and the formation impedance phaseis about −30 deg.

So for all these situations the only assumption that can be made is thatthe phases of the mud and formation impedances are different. However,an embodiment of the present invention seeks to discriminate against themud and to become only sensitive to the formation, thus allowing betterimaging in formations having low resistivity.

In order to make such a discrimination, it is necessary to determine thecomponent of the total impedance that is perpendicular to the phase ofthe mud impedance.

FIG. 6 shows a series of figures showing how such a discrimination ismade. Specifically, FIG. 6( a) shows the total impedance being the sumof the formation impedance Zf and the mud impedance Zm in series. FIG. 6b shows a vector diagram where the impedance vectors are plotting on aset of real and imaginary axes. These axes show the magnitude and phaseof each of the formation Zf and mud Zm impedance vectors and how thesesum to give the total impedance vector Z.

Finally, FIG. 6 c shows in accordance with an embodiment of theinvention that the total impedance Z is broken into components that areparallel and orthogonal to the mud. The parallel component is sensitivemainly to the mud and can be used as a qualitative indicator of buttonstandoff for quality control. The orthogonal component is completelyinsensitive to the mud and sensitive only to the formation.

Thus, knowing the mud phase (i.e. phase angle of the mud impedancevector) φ_(m), the orthogonal and parallel components can be calculatedusing standard rotation equations. The real and imaginary axes arerotated by 90+φ_(m) degrees to become the orthogonal and parallel axes,respectively.

According to an embodiment of the invention the mud phase is determinedby measuring the total impedance at two distances from the boreholewall, wherein the difference of the impedances represents the impedanceof the extra mud medium. In one embodiment this is achieved by adding anextra “mud” button, which is recessed to sit a few mm further from theborehole wall than the other imaging button(s).

An example of such a recessed mud button configuration according to anembodiment of the invention is shown in FIG. 9. Specifically, thecross-section view shows that the mud button 92 is recessed at aslightly further distance away from the borehole wall than the array ofimaging buttons 90 is spaced from the borehole wall. The array ofimaging buttons 90 in this embodiment is insulated from a surroundingguard electrode residing on a pad of the imaging tool, which is alignedadjacent to a face of the borehole.

The particular embodiment of FIG. 9 shows a double return-pad 96configuration, but it should be appreciated that a more basic embodimentas shown in FIG. 12 is equally possible. Indeed, FIG. 12 shows a basicembodiment comprising a single return pad 96′, a single recessed mudbutton 92′ and a single imaging button 90′.

FIGS. 7( a) and 7(b) shows the equivalents circuits as seen from theimaging and mud buttons respectively.

Specifically, the imaging button sees:

Z=Z _(m) +Z _(f),

whereas, the mud button sees

Z(b_mud)=Z _(m) +Z _(f) +ΔZ _(m)

and the difference is the extra mud impedance:

ΔZ _(m) =Z(b_mud)−Z

FIG. 8 shows this in vector form. The phase of the impedance φ_(m) iscalculated in the normal manner:

φ_(m)=tan⁻¹(Imag(ΔZ _(m))/Real(ΔZ _(m)))

Thus, the embodiment shown in FIG. 9 is a high frequency pad operatingin the range 1-100 MHz. The two recessed mud buttons 92 are of each ofsimilar size to the imaging buttons 90 and are surrounded by anequipotential guard electrode like the imaging buttons. A guard need notbe used in an alternative embodiment. In this way the mud buttonsmeasure an impedance very close to the impedance that would be measuredby the imaging buttons if the pad were further away from the boreholewall. ΔZ_(m) can be determined from the difference in impedancesmeasured by one imaging button and one mud button.

ΔZ_(m) is proportional to the distance by which the mud button 92 isrecessed. However, the phase of the mud impedance is not sensitive tothis distance so the technique does not need accurate knowledge of thedistance and it can cope with wear on the imaging electrode.

The mud buttons 92 are advantageously placed close to the imaging arrayand multiplexed into the same current amplification and detectionelectronics. This automatically corrects any phase errors in theelectronics (for example, due to high temperature downhole or inaccuratecalibration). A phase shift will rotate all the impedance vectors,including ΔZ_(m), by the same angle.

Moreover, the configuration of FIG. 9 or 12 allows errors in themeasurement to be reduced by calculating the average or median impedanceseen by the mud buttons and the average or median impedance seen by twoor more of the imaging buttons.

The formation impedance seen by the imaging button at an instant in timeis different from that seen by the mud button, because the measurementsare made at slightly different physical positions on the pad. The mudbutton measurement can be depth-shifted to the same depth as the imagingbuttons using well-known techniques. However, depth shifting is notnecessary since the mud properties are expected to vary slowly comparedto the formation properties. It is preferable (and simpler) to take theaverage or median of the measurements of both Z and Z(b_mud) over arange of depths of at least a meter in order to average the formationimpedance component.

There are alternative embodiments using recessed electrodes, for exampleinstead of using a recessed mud button and an imaging button, the mudimpedance may be measured using two mud buttons, one of which isrecessed compared to the other.

In another embodiment, instead of using a recessed mud button and animaging button, the mud impedance may be measured using two imagingbuttons, one of which is recessed compared to the other.

In another embodiment, the button(s) used to measure mud impedance mayhave different size and shape, the difference being corrected bycalculation.

In another embodiment, the processing technique of taking the mudmeasurement may be performed in oil-based mud, whether the tool isoriginally designed for water-based mud or oil-based mud. Imaging toolscapable of operating in the frequency range from about 1 kHz to 100 MHzare capable of being adapted for such mud measurement.

FIG. 15 shows yet another button placement embodiment, in which thereare two mud buttons on each side of the imaging button array 150. Atleast one of the mud buttons is recessed. An advantage of thisconfiguration is that the two mud buttons are each at the same distancefrom the return electrode so the impedance measurement taken of theformation can be averaged and hence made more accurate.

FIG. 16 shows yet another button placement embodiment, in which theguard electrodes 152 (shown in FIG. 15 is no longer present).Specifically, the configuration of FIG. 16 shows all the electrodes tobe located in a co-planar manner and on the same guard electrode 94.This configuration is advantageous in providing space saving on the pad.

FIG. 17 shows a profile of the pad which typically has a curvature shownby 170. However, it is possible to implement the embodiment of FIG. 16by taking a machine cut along line Z-Z to recess at least one of theelectrodes.

It should be appreciated that the embodiments of the invention arecapable to be adapted for use in wireline applications, for example bymounting the electrodes on pads or skids. The return electrode can be onthe same pad, on a different pad or on a tool mandrel or a combinationof these.

Alternatively, the imaging tools adapted to an embodiment of theinvention can be used in LWD (Logging While Drilling applications), forexample by mounting electrodes on a drill collar, stabiliser blade,rotating sleeve, pad or a combination of these. The return electrode canbe on the same pad, on an adjacent part of the drill collar, sleeve orstabilizer.

The guard electrode is not essential, especially when the formation ismore conductive than the mud, i.e. when the modulus of the formation ofthe formation conductivity is greater than the modulus of the mudconductivity. In such an embodiment, the current lines tend to be nearlyperpendicular to the borehole wall.

Thus, in an embodiment of the invention ΔZ_(m) is obtained bysubtracting the impedance from an electrode recessed from another, whichis in turn is used to determine the phase of the complex mud impedance.This in turn is used to establish the orthogonal impedance component,which provides a more accurate image for low resistivities formations.

Alternatively, in another embodiment, the mud impedance Zm can bemeasured differently in that the current travels directly from aninjector to a return via a volume of mud. In this embodiment theinjector and return electrode are separate from the main imagingelectrode. The injector and return electrodes can be co-planar (locatedon the same face of a pad) or be located face-to-face in a recess on apad, stabilizer or tool body. Specifically, FIG. 14 shows a pad with arecess notched out of its profile. The notch is shown to be of width d1.For this embodiment, it is necessary to either have a separate currentsource 190 or additional wiring/electronics that draw power from themain voltage source 180. By applying the separate voltage source 190across the notch, a potential difference is setup which causes a currentI2 to flow directly across the gap. Thus, this is an alternative methodof being able to deduce the impedance of the mud Zm provided mud isflowing in the borehole and into the notch.

Thus, the mud impedance is capable of being measured in different ways.The separate injector embodiment does not require further recessedbuttons, but requires slightly more space due to the separation needed.On the other hand the recessed electrode embodiment allows for closeplacement of the mud button to the imaging button. This allows for themultiplexing of the electronics, which not only saves space butautomatically allows for correction of phase shifts in the electronics.

FIGS. 10 and 11 show results of the mud impedance measurement andorthogonal processing performed on lab data. The pad used for thesemeasurements was not equipped with extra recessed mud buttons. Instead,the impedance measured by the imaging buttons at a greater standoff wasused to simulate the recessed buttons.

Specifically, FIG. 10 shows a block of artificial rock containing bedsof resistivities from 0.2 to 30 Ω·m. The block was scanned with animaging tool at a frequency above 1 MHz in oil-based mud. Images 1 to 3from the left show the amplitude measurement at three standoffs: 1, 2and 4 mm, and images 4 to 6 show the phase measurement at threestandoffs. Both amplitude and phase are affected by standoff.

FIG. 11 shows the impedance components for the same data set. Images 1to 3 from the left show the orthogonal component and images 4 to 6 showthe parallel component. The images showing orthogonal component ofimpedance are almost unaffected by standoff and are weakly sensitive tothe two parallel mud-filled grooves at the top of the image.

According to another embodiment of the invention, the obtained ΔZ_(m) isused to also determine other properties.

For example, in one embodiment the ΔZ_(m) measurement is used tocalculate the complex conductivity of the mud provided the geometry ofthe mud button is accurately known.

σ*=Δd _(m)/(A _(m) ·ΔZ _(m))

where Δd_(m) is the distance by which the mud button is recessed andA_(m) is the effective area of the button.

From the complex conductivity, it is possible to then determine thereal-valued conductivity, permittivity and resistivity of the formationusing standard equations:

σ=Real(σ*)

∈=Imag(σ*)/ω

where σ is the conductivity, ∈ the permittivity.

When the material is highly conductive, the real-valued resistivity isgiven by

ρ=1/σ

It is possible to use more than one frequency (simultaneously orsequentially) to optimise the measurement sensitivity to the mud orformation. To determine the standoff of the imaging buttons it ispreferable to use a relatively low frequency (for example from about 10kHz to 1 MHz) so that the imaging buttons are much more sensitive to themud than the formation (Z_(m)>>Z_(f)).

From the measured mud complex conductivity, it is also possible todetermine the standoff for each imaging button at a low frequency asfollows:

d _(m) =A _(m) ·|Z _(m)·σ*|

To image the formation it is preferable to use higher frequencies thatare less sensitive to the mud. For the lowest resitivity formations(below 1 Ω·m), a frequency in the range 10-100 MHz is preferable, whilefor high resistivities above 100 Ω·m a frequency in the range of 100 kHzto 1 MHz suffices. It should be understood that these frequency rangescould alter depending on electronic and processing improvements.

In turn, the standoff and complex mud conductivity can be used in otherprocessing algorithms to determine the formation properties.

The standoff can be used for quality control of the measurements. Thestandoff can also be used to improve the accuracy of hole radiusmeasurements.

In the embodiment of a wireline tool with several pads pressed againstthe borehole wall, by taking the sum of the mechanically measured padradius and the standoff on each imaging button a detailed hole shapeimage can be produced. FIG. 18 shows an embodiment of this where aplurality of electrodes are 182, 184, 186, 188 are mounted on a pad, allcapable of injecting current into the formation which completes its pathto the return pad 181. The electrodes 182, 184, 186 and 188 are shown tomeasure the standoffs S1, S2, S3, and S4 respectively. It is thenpossible for these respective standoff measurements to be combined toallow a profile or shape of the actual borehole wall to be constructed.

In the embodiment of a rotating LWD tool, the standoff can be used todetermine the position of the tool relative to the borehole wall, and iftwo diametrically opposed buttons are used the hole diameter can bedetermined at each azimuthal position.

FIG. 13 shows an overview of a wireline application where an embodimentof the invention may be applied. Specifically, an imaging tool 135,equipped for example with a pad 137, is suspended from a wireline cable132 downhole. The borehole 2 is surrounded by the earth formation 4. Theimaging tool sends imaging information to surface equipment 130.

To summarise some of the embodiments described, one embodiment of theinvention is concerned with orthogonal processing, wherein the componentof the mud impedance phase that is orthogonal to the total impedance isdetermined. This improves imaging especially in oil-based mud in lowresisitivity formations.

Another embodiment of the invention is concerned with determining themud impedance phase from the difference in impedances measured by twoelectrodes arranged at different distances from the borehole wall.

Another embodiment is concerned with using the mud impedance obtainedfrom recessed mud electrodes to determine other formation propertiessuch as the mud conductivity or standoff or for improving the accuracyof the borehole radius measurements.

Another embodiment is concerned with determining the mud impedance phasedirectly from current passing directly across a notch in the pad withoutentering the formation.

Thus it is possible to obtain accurate images when the formationimpedance is less than the mud impedance. This is achieved bydiscriminating against the mud by measuring the phase of the complex mudimpedance and calculating the component of the total complex impedanceorthogonal to the mud phase. The phase angle of the mud impedance ispreferably measured from the difference between the impedances measuredby two electrodes at different distances from the formation. Preferably,one of the difference electrodes is an imaging electrode and the otheris an additional “mud” electrode situated close to it and recessed so asto be at a greater distance from the formation. However, otherconfigurations have also been described.

1. A tool for imaging a formation through a substantially non-conductivemedium, the tool comprises: first circuitry for injecting a current intothe formation, wherein a complex impedance to the current is measured;second circuitry for determining a phase angle of an impedance of thenon-conductive medium; and third circuitry for determining a componentof the complex impedance that is orthogonal to the phase angle.
 2. Thetool of claim 1, wherein the first circuitry comprises: a firstelectrode for injecting the current in the formation; and a receiveelectrode for receiving the current.
 3. The tool of claim 2, where thecurrent is injected in the formation as a result of a voltage differencebetween the first electrode and the receive electrode.
 4. The tool ofclaim 3, wherein the voltage difference is generated by a generatorcapable of generating an alternating voltage at a desired frequency. 5.The tool of claim 3, wherein the tool is capable of determining anin-phase and a quadrature component of the current and the voltage. 6.The tool of claim 2, wherein the second circuitry comprises: a secondelectrode for injecting a second current in the formation, the secondelectrode is located on the tool at a different distance from theformation as compared to the first electrode, wherein a second compleximpedance to the second current is determined; and a processor fordetermining the phase angle from a difference between the compleximpedance and the second complex impedance.
 7. The tool of claim 6,wherein the second electrode is at least one of an imaging button, a mudbutton and one of an array of buttons.
 8. The tool of claim 6, whereinthe phase angle φ_(m) is determined from the difference ΔZ_(m) by:φ_(m)=tan⁻¹(Imag(ΔZ _(m))/Real(ΔZ _(m)))
 9. The tool of claim 2, whereinthe first electrode is at least one of an imaging button, a mud buttonand one of an array of buttons.
 10. The tool of claim 1, wherein thenon-conductive medium is oil-based mud.
 11. The tool of claim 1, whereinthe formation has a resistivity that is sufficiently low that animpedance of the formation is less than an impedance of thenon-conducting medium.
 12. The tool of claim 1, wherein the thirdcircuitry is further capable of determining a component of the compleximpedance that is parallel to the phase angle for qualitative indicationof a standoff.
 13. A method for measuring a component of an impedance ofa formation through a substantially non-conductive medium, the methodcomprising: injecting a current in the formation; measuring a compleximpedance to the current; determining a phase angle of an impedance ofthe non-conductive medium; and determining the component of the compleximpedance that is orthogonal to the phase angle.